You can mix Talstar P with Precor IGR for flea control. According to the new Talstar P product label you can make applications as spot or crack and crevice treatments to areas frequented by pets, such as under bedding, rugs, next to furniture. Vacuum prior to treatment.
What this means is that you cannot broadcast spray your entire carpet with Talstar, you must limit the treatment to "spot" treatments (areas that 2ft x 2ft or less). If you only need to spot treat certain areas you can use Talstar for fleas. If you need to broadcast over entire carpeted rooms you should choose a product which is labeled for indoor broadcast sprays such as Onslaught or Permethrin SFR.
There is no real reason to mix both Talstar and Cyper. They kill pretty much the same insects. One or the other would most likely do the job.